Proportion of Missing Values

The following presents more details on the proportion of missing values used in the simulation study.

library(manMCMedMiss)

Data Generation

n <- 1000
tauprime <- 0
alpha <- 0.5
beta <- 0.5

set.seed(42)
data_complete <- GenData(
  n = n,
  tauprime = tauprime,
  beta = beta,
  alpha = alpha
)

Amputation

prop <- 0.30
data_missing <- AmputeData(
  data_complete,
  mech = "MCAR",
  prop = prop
)

Missing Data Patterns

The matrix below shows the missing data patterns in the amputed data.

mice::md.pattern(data_missing)

#>       m   x   y    
#> 724   1   1   1   0
#> 42    1   1   0   1
#> 45    1   0   1   1
#> 54    1   0   0   2
#> 43    0   1   1   1
#> 50    0   1   0   2
#> 42    0   0   1   2
#>     135 141 146 422

Proportion of missing values by row

This is the number of rows with missing values divided by the total number of rows. This is the value of the prop argument in AmputeData() which is a wrapper around the mice::ampute() function.

sum_row <- sum(!complete.cases(data_missing))
prop_row <- sum_row / n
c(
  sum_row = sum_row,
  prop_row = prop_row
)
#>  sum_row prop_row 
#>  276.000    0.276

Proportion of missing values by column

This is the number of rows per column with missing values divided by the total number of rows.

sum_col <- colSums(is.na(data_missing))
names(sum_col) <- paste0(
  "sum_col_",
  names(sum_col)
)
prop_col <- sum_col / n
names(prop_col) <- gsub("sum", "prop", names(sum_col))
c(
  sum_col,
  prop_col
)
#>  sum_col_x  sum_col_m  sum_col_y prop_col_x prop_col_m prop_col_y 
#>    141.000    135.000    146.000      0.141      0.135      0.146

Proportion of missing values by cell

This is the number of cells with missing values divided by the number of rows times the number of columns.

sum_cell <- sum(is.na(data_missing))
prop_cell <- sum_cell / (n * 3)
prop_cell
#> [1] 0.1406667
c(
  sum_cell = sum_cell,
  prop_cell = prop_cell
)
#>    sum_cell   prop_cell 
#> 422.0000000   0.1406667

Empirical Proportion of Missing Values

Below is a simple simulation to show the empirical proportions for the combination of sample size n and prop used in the study for 5000 replications.

MAR

n	prop	sum_row	prop_row	sum_col_x	sum_col_m	sum_col_y	prop_col_x	prop_col_m	prop_col_y	sum_cell	prop_cell	reps
50	0.1	4.91	0.1	2.47	2.46	2.45	0.05	0.05	0.05	7.37	0.05	5000
75	0.1	7.43	0.1	3.71	3.73	3.70	0.05	0.05	0.05	11.14	0.05	5000
100	0.1	10.04	0.1	5.01	5.01	5.04	0.05	0.05	0.05	15.06	0.05	5000
150	0.1	15.02	0.1	7.48	7.48	7.54	0.05	0.05	0.05	22.51	0.05	5000
200	0.1	19.81	0.1	9.89	9.87	9.90	0.05	0.05	0.05	29.66	0.05	5000
250	0.1	24.91	0.1	12.45	12.46	12.42	0.05	0.05	0.05	37.33	0.05	5000
500	0.1	50.00	0.1	25.04	24.94	25.06	0.05	0.05	0.05	75.03	0.05	5000
1000	0.1	100.13	0.1	50.21	49.96	49.97	0.05	0.05	0.05	150.15	0.05	5000
50	0.2	9.87	0.2	4.94	4.95	4.92	0.10	0.10	0.10	14.81	0.10	5000
75	0.2	14.90	0.2	7.43	7.46	7.47	0.10	0.10	0.10	22.37	0.10	5000
100	0.2	19.91	0.2	9.95	9.96	9.99	0.10	0.10	0.10	29.89	0.10	5000
150	0.2	30.05	0.2	15.04	15.03	15.06	0.10	0.10	0.10	45.13	0.10	5000
200	0.2	39.84	0.2	19.88	19.89	19.96	0.10	0.10	0.10	59.72	0.10	5000
250	0.2	49.88	0.2	25.06	24.89	24.83	0.10	0.10	0.10	74.78	0.10	5000
500	0.2	100.03	0.2	49.95	50.07	50.00	0.10	0.10	0.10	150.01	0.10	5000
1000	0.2	200.17	0.2	100.40	99.96	99.89	0.10	0.10	0.10	300.26	0.10	5000
50	0.3	14.85	0.3	7.42	7.39	7.43	0.15	0.15	0.15	22.24	0.15	5000
75	0.3	22.35	0.3	11.17	11.16	11.23	0.15	0.15	0.15	33.56	0.15	5000
100	0.3	29.86	0.3	14.90	14.95	14.95	0.15	0.15	0.15	44.81	0.15	5000
150	0.3	44.88	0.3	22.40	22.53	22.48	0.15	0.15	0.15	67.41	0.15	5000
200	0.3	60.06	0.3	30.04	29.98	30.08	0.15	0.15	0.15	90.10	0.15	5000
250	0.3	74.75	0.3	37.53	37.33	37.25	0.15	0.15	0.15	112.11	0.15	5000
500	0.3	149.97	0.3	74.87	75.20	74.93	0.15	0.15	0.15	224.99	0.15	5000
1000	0.3	299.77	0.3	150.08	149.76	149.83	0.15	0.15	0.15	449.68	0.15	5000

MCAR

n	prop	sum_row	prop_row	sum_col_x	sum_col_m	sum_col_y	prop_col_x	prop_col_m	prop_col_y	sum_cell	prop_cell	reps
50	0.1	4.99	0.1	2.49	2.49	2.50	0.05	0.05	0.05	7.48	0.05	5000
75	0.1	7.47	0.1	3.74	3.74	3.71	0.05	0.05	0.05	11.20	0.05	5000
100	0.1	10.01	0.1	4.99	4.99	5.02	0.05	0.05	0.05	15.00	0.05	5000
150	0.1	15.05	0.1	7.51	7.52	7.52	0.05	0.05	0.05	22.56	0.05	5000
200	0.1	20.03	0.1	10.11	10.02	9.94	0.05	0.05	0.05	30.08	0.05	5000
250	0.1	25.04	0.1	12.52	12.51	12.54	0.05	0.05	0.05	37.57	0.05	5000
500	0.1	50.11	0.1	25.01	25.15	24.99	0.05	0.05	0.05	75.15	0.05	5000
1000	0.1	100.08	0.1	50.13	49.99	50.02	0.05	0.05	0.05	150.14	0.05	5000
50	0.2	9.99	0.2	5.03	4.97	5.00	0.10	0.10	0.10	15.00	0.10	5000
75	0.2	14.94	0.2	7.49	7.45	7.44	0.10	0.10	0.10	22.38	0.10	5000
100	0.2	19.99	0.2	9.97	9.97	10.01	0.10	0.10	0.10	29.95	0.10	5000
150	0.2	30.04	0.2	15.05	14.98	15.00	0.10	0.10	0.10	45.03	0.10	5000
200	0.2	40.04	0.2	20.09	20.04	19.97	0.10	0.10	0.10	60.10	0.10	5000
250	0.2	50.05	0.2	25.08	25.04	25.02	0.10	0.10	0.10	75.14	0.10	5000
500	0.2	100.09	0.2	49.98	50.13	49.99	0.10	0.10	0.10	150.11	0.10	5000
1000	0.2	200.09	0.2	100.06	100.02	99.93	0.10	0.10	0.10	300.02	0.10	5000
50	0.3	15.02	0.3	7.52	7.50	7.49	0.15	0.15	0.15	22.51	0.15	5000
75	0.3	22.47	0.3	11.27	11.22	11.19	0.15	0.15	0.15	33.67	0.15	5000
100	0.3	29.99	0.3	15.00	14.96	14.97	0.15	0.15	0.15	44.93	0.15	5000
150	0.3	45.05	0.3	22.60	22.46	22.47	0.15	0.15	0.15	67.54	0.15	5000
200	0.3	60.11	0.3	30.15	30.03	30.01	0.15	0.15	0.15	90.20	0.15	5000
250	0.3	75.06	0.3	37.61	37.51	37.50	0.15	0.15	0.15	112.62	0.15	5000
500	0.3	150.10	0.3	75.06	75.05	74.99	0.15	0.15	0.15	225.10	0.15	5000
1000	0.3	300.14	0.3	150.09	150.00	150.00	0.15	0.15	0.15	450.09	0.15	5000

Code to perform the simulation.

bar <- function(mech) {
  foo <- function(x,
                  reps = 5000,
                  mech,
                  seed = 42) {
    set.seed(42)
    n <- x[1]
    prop <- x[2]
    data_complete <- GenData(n = n)
    colMeans(
      do.call(
        what = "rbind",
        args = lapply(
          X = 1:reps,
          FUN = function(i, mech) {
            data_missing <- AmputeData(
              data_complete,
              mech = mech,
              prop = prop
            )
            sum_row <- sum(!complete.cases(data_missing))
            prop_row <- sum_row / n
            row <- c(
              sum_row = sum_row,
              prop_row = prop_row
            )
            sum_col <- colSums(is.na(data_missing))
            names(sum_col) <- paste0(
              "sum_col_",
              names(sum_col)
            )
            prop_col <- sum_col / n
            names(prop_col) <- gsub("sum", "prop", names(sum_col))
            col <- c(
              sum_col,
              prop_col
            )
            sum_cell <- sum(is.na(data_missing))
            prop_cell <- sum_cell / (n * 3)
            prop_cell
            cell <- c(
              sum_cell = sum_cell,
              prop_cell = prop_cell
            )
            c(
              n = n,
              prop = prop,
              row,
              col,
              cell,
              reps = reps
            )
          },
          mech = mech
        )
      )
    )
  }
  do.call(
    what = "rbind",
    args = lapply(
      X = as.data.frame(
        t(
          expand.grid(
            n = unique(manMCMedMiss::params$n),
            prop = 1:3 * .10
          )
        )
      ),
      FUN = foo,
      mech = mech
    )
  )
}
prop_mar <- bar("MAR")
prop_mcar <- bar("MCAR")

Ivan Jacob Agaloos Pesigan